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Simplifying 9x2 + -49x + 4 = 0 Reorder the terms: 4 + -49x + 9x2 = 0 Solving 4 + -49x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + -5.444444444x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -5.444444444x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -5.444444444x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -5.444444444x + x2 = 0 + -0.4444444444 -5.444444444x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -5.444444444x + x2 = -0.4444444444 The x term is -5.444444444x. Take half its coefficient (-2.722222222). Square it (7.410493826) and add it to both sides. Add '7.410493826' to each side of the equation. -5.444444444x + 7.410493826 + x2 = -0.4444444444 + 7.410493826 Reorder the terms: 7.410493826 + -5.444444444x + x2 = -0.4444444444 + 7.410493826 Combine like terms: -0.4444444444 + 7.410493826 = 6.9660493816 7.410493826 + -5.444444444x + x2 = 6.9660493816 Factor a perfect square on the left side: (x + -2.722222222)(x + -2.722222222) = 6.9660493816 Calculate the square root of the right side: 2.639327449 Break this problem into two subproblems by setting (x + -2.722222222) equal to 2.639327449 and -2.639327449.Subproblem 1
x + -2.722222222 = 2.639327449 Simplifying x + -2.722222222 = 2.639327449 Reorder the terms: -2.722222222 + x = 2.639327449 Solving -2.722222222 + x = 2.639327449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.722222222' to each side of the equation. -2.722222222 + 2.722222222 + x = 2.639327449 + 2.722222222 Combine like terms: -2.722222222 + 2.722222222 = 0.000000000 0.000000000 + x = 2.639327449 + 2.722222222 x = 2.639327449 + 2.722222222 Combine like terms: 2.639327449 + 2.722222222 = 5.361549671 x = 5.361549671 Simplifying x = 5.361549671Subproblem 2
x + -2.722222222 = -2.639327449 Simplifying x + -2.722222222 = -2.639327449 Reorder the terms: -2.722222222 + x = -2.639327449 Solving -2.722222222 + x = -2.639327449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.722222222' to each side of the equation. -2.722222222 + 2.722222222 + x = -2.639327449 + 2.722222222 Combine like terms: -2.722222222 + 2.722222222 = 0.000000000 0.000000000 + x = -2.639327449 + 2.722222222 x = -2.639327449 + 2.722222222 Combine like terms: -2.639327449 + 2.722222222 = 0.082894773 x = 0.082894773 Simplifying x = 0.082894773Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.361549671, 0.082894773}
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